Question

The weights of newborn elephants are normally distributed with a mean of 225 pounds and a standard deviation of 45 pounds. a) Find the probability that a newborn elephant weighs between 250 and 275 pounds. You must show your work using a calculator function to receive credit. b) Find the probability that a newborn elephant weighs more than 210 pounds. You must show your work using a calculator function to receive credit.

Answer 1

a)

The probability that a newborn elephant weighs between 250 and 275 pounds

P(250≤ x ≤275) = 0.1577

b)

The probability that a newborn elephant weighs more than 210 pounds

P(x >210 ) = 0.6293

Explanation:

Step(i):-

Given mean of the Population = 225

Given standard deviation of the population = 45

Let 'X' be the random variable in normal distribution

Let x₁ = 250

`Z = (x-mean)/(S.D) = (250-225)/(45) = 0.55`

Let x₂ = 275

`Z = (x-mean)/(S.D) = (275-225)/(45) = 1.11`

The probability that a newborn elephant weighs between 250 and 275 pounds

P(250≤ x ≤275) =P(0.55≤ Z≤1.11)

= P(Z≤1.11) - P(Z≤0.55)

= 0.5 + A( 1.11) - ( 0.5 + A(0.55)

= A(1.11) - A(0.55)

= 0.3665 - 0.2088

= 0.1577

Step(ii):-

The probability that a newborn elephant weighs between 250 and 275 pounds

P(250≤ x ≤275) = 0.1577

b)

Let x = 210

`Z = (x-mean)/(S.D) = (210-225)/(45) = - 0.33`

The probability that a newborn elephant weighs more than 210 pounds

P(x >210 ) = P( Z> -0.33)

= 1- P( Z < -0.33)

= 1 - ( 0.5 - A(-0.33))

= 0.5 + A( -0.33)

= 0.5 + A(0.33) (∵ A(-0.33) = A(0.33)

= 0.5 + 0.1293

= 0.6293

Final answer:-

The probability that a newborn elephant weighs more than 210 pounds

P(x >210 ) = 0.6293